Exercises 31–34 display a matrix A and an echelon form of A . Find a basis for Col Aand a basis for Nul A . In this example, we have a problem from linear algebra pertaining to matrices.The matrix \( A \) is given as:\[A = \begin{bmatrix}1 & 4 & 8 & -3 & -7 \\-1 & 2 & 7 & 3 & 4 \\-2 & 2 & 9 & 5 & 5 \\3 & 6 & 9 & -5 & -2\end{bmatrix}\]The matrix \( A \) undergoes row operations to reach its row echelon form:\[\sim \begin{bmatrix}1 & 4 & 8 & 0 & 5 \\0 & 2 & 5 & 0 & -1 \\0 & 0 & 1 & 0 & 4 \\0 & 0 & 0 & 0 & 0\end{bmatrix}\]Explanation of the procedure:1. The matrix \( A \) is a \( 4 \times 5 \) matrix.2. Through a series of row operations (which typically includes row swapping, row multiplication, and row addition/subtraction), the initial matrix is transformed to a row echelon form. 3. The leading entries (also known as pivots), which are the first non-zero numbers in each row, are aligned in a stair-step fashion from left to right.Importantly, the matrix can have zero rows at the bottom, indicating rows of all zeroes which are a result of the row operations to move to echelon form.These steps help in solving systems of linear equations and understanding the properties of matrix transformations.

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Answered: 33. A = 1 4 8 -3 -7 -1 2 7 3 4 -2 29 5…

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33. A = 1 4 8 -3 -7 -1 2 7 3 4 -2 29 5 5 369-5 -2 1 4 80 5 0250 −1 0 0 0 1 4 0000 0

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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Question

Exercises 31–34 display a matrix A and an echelon form of A . Find a basis for Col Aand a basis for Nul A .

In this example, we have a problem from linear algebra pertaining to matrices.

The matrix \( A \) is given as:

\[
A = \begin{bmatrix}
1 & 4 & 8 & -3 & -7 \\
-1 & 2 & 7 & 3 & 4 \\
-2 & 2 & 9 & 5 & 5 \\
3 & 6 & 9 & -5 & -2
\end{bmatrix}
\]

The matrix \( A \) undergoes row operations to reach its row echelon form:

\[
\sim \begin{bmatrix}
1 & 4 & 8 & 0 & 5 \\
0 & 2 & 5 & 0 & -1 \\
0 & 0 & 1 & 0 & 4 \\
0 & 0 & 0 & 0 & 0
\end{bmatrix}
\]

Explanation of the procedure:
1. The matrix \( A \) is a \( 4 \times 5 \) matrix.
2. Through a series of row operations (which typically includes row swapping, row multiplication, and row addition/subtraction), the initial matrix is transformed to a row echelon form.
3. The leading entries (also known as pivots), which are the first non-zero numbers in each row, are aligned in a stair-step fashion from left to right.

Importantly, the matrix can have zero rows at the bottom, indicating rows of all zeroes which are a result of the row operations to move to echelon form.

These steps help in solving systems of linear equations and understanding the properties of matrix transformations.

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